Accuracy problems associted with semi-analytical derivatives of static response

SUMMARYThe present paper focuses on the evaluation of the shape sensitivities of the limit and bifurcation loads of geometrically non-linear structures. The analytical approach is applied for isoparametric elements, leading to exact results for a given mesh. Since this approach is di cult to apply to other element types, the semi-analytical method has been widely used for shape sensitivity computation. This method combines ease of implementation with computational e ciency, but presents severe accuracy problems. Thus, a general procedure to improve the semi-analytical sensitivities of the non-linear critical loads is presented. The numerical examples show that this procedure leads to sensitivities with su cient accuracy for shape optimization applications.

Section: Semi-analytical Methods (Sam)mentioning

confidence: 94%

On evaluation of shape sensitivities of non‐linear critical loads

Parente

Vaz

2002

“…It has been shown that such errors occur when the displacement ÿeld is dominated by the rigid body rotations of individual elements. This behaviour occurs in linear [4][5][6] as well as non-linear [3] structures.…”

Section: Introductionmentioning

confidence: 99%

“…In the conventional semi-analytical method, these derivatives are usually evaluated by means of the forward ÿnite di erence scheme. This procedure has been recognized as the source of errors in the semi-analytical method [4][5][6]. Three di erent approaches have been proposed to solve this problem.…”

Section: Introductionmentioning

confidence: 99%

Improvement of semi‐analytical design sensitivities of non‐linear structures using equilibrium relations

Parente

Vaz

2001

SUMMARYThe accuracy problem of the semi-analytical method for shape design sensitivity analysis has been reported for linear and non-linear structures. The source of error is the numerical di erentiation of the element internal force vector, which is inherent to the semi-analytical approach. Such errors occur for structures whose displacement ÿeld is characterized by large rigid body rotations of individual elements. This paper presents a method for the improvement of semi-analytical sensitivities. The method is based on the element free body equilibrium conditions, and on the exact di erentiation of the rigid body modes. The method is e cient, simple to code, and can be applied to linear and non-linear structures. The numerical examples show that this approach eliminates the abnormal errors that occur in the conventional semi-analytical method.

“…Di erent techniques have been used to tackle the accuracy problem. Popular techniques are the higher order or alternative ÿnite di erence schemes, for example References [6][7][8]. The method presented in Reference [9] is based on the 'natural approach' and consistency conditions for rigid body modes (RBM).…”

Section: Introductionmentioning

confidence: 99%

Refined second order semi‐analytical design sensitivities

Boer

Keulen

Vervenne

2002

SUMMARYAccurate and e cient calculation of second order design sensitivities in a ÿnite element context is often di cult. The semi-analytical (SA) method is e cient and easy to implement but has accuracy problems even for ÿrst order shape design sensitivities. To overcome accuracy problems a reÿned semianalytical (RSA) method has been developed for ÿrst order sensitivities. The present paper investigates the application of the RSA method to second order design sensitivities. It is found that second order RSA sensitivities are signiÿcantly more accurate than their SA counterparts.